Problema Solution
The perimeter of a triangle is 105 inches. The longest side is 22 inches longer than the shortest side. The sum of the lengths is 15 inches more than the length of the longest side. Find the length of the sides of the triangle.
Answer provided by our tutors
The problem has solution only if the sentence " The sum of the lengths is 15 inches more than the length of the longest side." is replaced with the sentence "The sum of the lengths of the shortest and the middle side is 15 inches more than the length of the longest side."
Let a, b and c represent the lengths of the sides of the triangle and a<b<c that is:
a = the shortest side
b = the middle side
c = the longest side
The perimeter of a triangle is 105 inches:
a + b + c = 105
The longest side is 22 inches longer than the shortest side:
c = 22 + a
The sum of the lengths of the shortest and the middle side is 15 inches more than the length of the longest side:
a + b = 15 + c
By solving the system of equations:
a + b + c = 105
c = 22 + a
a + b = 15 + c
........
........
a = 23 in
b = 37 in
c = 45 in
The lengths of the sides of the triangle are: 23 inches, 37 inches and 45 inches.